High Anxieties: The Mathematics of Chaos

The documentary looks at the modern advances in mathematics and how they affect our understanding of physics, economics, environmental issues and human psychology.

The film looks at how developments in 20th Century mathematics have affected our view of the world, and particularly how the financial economy and earth’s environment are now seen as inherently unpredictable.

The film looks at the influence the work of Henri Poincare and Alexander Lyapunov had on later developments in mathematics. It includes interviews with David Ruelle, about chaos theory and turbulence, the economist Paul Ormerod about the unpredictability of economic systems, and James Lovelock the founder of Gaia theory about climate change and tipping points in the environment.

As we approach tipping points in both the economy and the climate, the film examines the mathematics we have been reluctant to face up to and asks if, even now, we would rather bury our heads in the sand rather than face harsh truths.

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62 Comments / User Reviews

knowledgeizpower

This is a great one to view, especially touching on the weather issues and the technology used to basically modify the climate. When you have discussions about such things as HAARP, some people just don't believe that this is being done or its possible they just think you're flipping crazy. They want to blame alot of this catastrophic weather on mother nature or if they believe in God its all His fault. No not neccesarily, if you look at it from a mathematical point of view hmmm what can the human species control if they put there minds to it..Well a hell of alot!

Should they control it NOOO because they don't know what the hell they're doing!! Damn Humans Will Blow us All Off The Face Of The Earth! By God Or by Man you choose which one to believe Lol, but you must agree with me when I say this....The way things are going if you want to look at it from a spiritual mathematical or a scientific point of view this Earth is pretty much screwed for survival.

Robert M

This had less to do with math then I was hoping, their unpredictable is quite predictable I think...

Jane Doe

The Earth will be just fine, we're only hurting ourselves.

Guest

the earth does eat up what ever mess we leave around, us included.
az

Earthwinger

Nothing particularly new here, but I found the way it was all put into an historical context, quite interesting. And I was heartened to see that they gave the last word to James Lovelock, who I have a great deal of respect for.

Luyang Han

The mathematical language of chaos is completely neutral, but this doc takes a completely negative interpretation of chaos, as uneasy, anxious, unsafe. And chaos is related to bad things such as hurricane and financial crisis, as if chaos is just evil and do bad things. This completely contradicts the new mathematical and scientific understanding of non-linearity and chaos, where chaotic phenomenon found huge applications. As an example, modern communication relies heavily on the chaotic theory. On a larger scale, the evolution of life itself is also a chaotic process. For my point of view, this doc's philosophical but naive view on scientific issues is highly misleading.

Epicurus

HAARP is not for controlling the weather. that is conspiracy theory nonsense.

there are other methods we have for controlling weather such as cloud seeding, but not HAARP.

Vlatko

I fully agree @Luyang Han. Well said.

knowledgeizpower

But the point is...is that the weather can be controlled would you agree on that?

Earthwinger

You're absolutely right in what you say about chaos theory, but as I see it, the doc was clear from the outset that the intention was to look at how our deeper understanding of the subject, has gone on to shape views in a couple of key areas. Which is exactly what they did.

Achems_Razor

True enough, we live in the midst of chaos, we happen to be riding on the one vibrational unit/wave, amidst the infinite sea of probabilities, probable actions, that make up our universe.

Epicurus

ya i think i remember seeing that the chinese were playing with cloud seeding when they held the olympics. and yes that is dangerous. changing the weather will have drastic effects on the rest of the ecosystem

knowledgeizpower

Yeah I agree its very dangerous i think they should stop messing around with the climate before they mess something up.

Guest

The ultimate chaos is death and perhaps the next ultimate chaos is birth in something entirely innimaginable.
Good doc...i need a second viewing
az

NAND Gate

It is refreshing to see someone make a valid comment like this.

hungrinow

Well said Jane. We are nothing short of embarrassingly vain in our belief that we will somehow destroy the earth....Mother will be here long enough after we're gone (if that is to be our destiny), to erase all evidence of humanity.

norlavine

@Epicurus
My vote is to pass right on through the ionosphere on the way to somewhere else. Too dangerous to mess with, but, I guess the sense of power once all military systems are go will make the important people happy for ten minutes.No conspiracy, just megalomania.

Philio

So, in a world of ultimate cause and ultimate effect, the ultimate cause is a fluctuation in chaotic movement that compounds within it’s self. Contained within the word chaos is the word unpredictability. Therefore every plan and every tweak imagined by the human mind is ultimately doomed to failure as the plan is formulated on the observed events caused by chaos.

The plan, itself, then only serves to increase chaos. The plan also serves to mitigate fear in a population and give the illusion of stability. The illusion can be manipulated to move a population toward another series of chaotic episodes. Ultimately it’s a case of the blind being led by the blind, so much so for leaders and followers.

Nature has always had its own answer to chaos, adapt or go extinct.

Damon Rolnick

you hit on something important- Death is considered in our culture to mean - NON-BEING
but if death is non-being then one cannot BE dead

however death IS a state of being and most people are, in fact dead- it isnt until you face death that you realize it as illusory and you wake up ALIVE for the first time

Upon awaking you are the only one left on the planet, you are realized as the creator of this reality and you are ONE with ALL- you are God-

N B

Fascinating subject. In many ways, the study of complexity and chaos represents the cutting edge of science and engineering, and it certainly offers some very big challenges. However, I do not share the somewhat fatalistic view that was expressed by the narrator. Mainly, I do not agree with the implication that complex or chaotic systems cannot be controlled. In fact we control many such systems already through the use of feedback control methodologies. Feedback control simply means that the controlled system is monitored and corrected whenever it begins to diverge from the desired behavior. Doing this requires only approximate knowledge of localized system dynamics (although it's true that a better understanding of the system dynamics usually allows us to design a better controller). So a properly controlled chaotic system would never have the opportunity to diverge or reach its tipping point, because it would have long since been corrected away form that particular state by the control system. Similarly, a complex system is usually controlled by breaking it into many simpler subsystems, each with a controller responsible only for the performance of that subsystem and for its interactions with the immediate neighborhood of other subsystems.

Obviously there are many systems that we cannot currently control. The weather has been correctly pointed out as one of them, and the economy is another glaring example. But just because we don’t know how to control them now doesn’t mean we never will. In my opinion, that means we shouldn’t be discourage from trying (as long as we go slow and are VERY careful).

Guest

That's kind of what i am saying, the two ultimate chaos are basically attached, one gives instant rise to the other. I can represent it by a vesica pisces. It is as if we are traversing from one reality to the other through a double wall chaos contained within those realities.

That was fun...and yes you can have a go at it

az

Guest

Death is death of life as we know it. If i step on an ant or if a person dies on a hospital bed, it has no more life.
In my view it has died to life but it may have birth into death. That i do not know until my self goes that way.
az

Guest

I may not have paid attention, as i wrote earlier i need an other viewing, but it seemed that he describes Chaos as an opportunity to change. Greater changes are most often the outcome of uneasy and anxious event followed by easier and calmer events until chaos happens inevitably again in one way or an other (often very unpredictably) and brings again a different kind of crisis...and so on and so on..
Life is a waxing and waning chaotic process even in our own personal life.
az

Achems_Razor

Azilda, You may know more about sacred geometry than I, but Vesica Pisces is still used by Christianity as their sign of the fish, which they attribute to the miraculous feeding of the fish, turning water to wine, loafs of bread as in Jesus, and so on.
Am curious as to how you present VP as one reality to another.

Yes, you may view a lifeless body, and I have witnessed many, since I was in an occupation to try and save lives, the success rate is never 100% of course.
That is all third hand experience when you witness death, can never be first hand experience can it?

Try to imagine a state where nothing exists. Such a state is impossible even contradictory, since the concept existence is necessary to apprehend it. Therefore existence exists necessarily, even if nothing else exists.

Guest

I was suggesting that you look at it as a graphic symbol.
As you look at the Vesica Pisces you have to imagine an infinite line of connected dots (or moments of life) travelling through VP from one side to the other.
In my analogy Life is represented by the passing through the first circle, the shared almond portion which is connected to the two realities is where death and rebirth are contained (representing ultimate chaos) until the doted line enters the other reality entirely.
az

Norm

Humans try to control everything yet we can't even control ourselves most of the time. I'm no expert but I can only see these feedback control systems working on autonomous mechanical or electronic systems. Applying this to a living system (nature, humans, etc..) would be fruitless wouldn't it?

Truthseeker420

Sometimes there are "tipping points" in our minds. The system changes and you can't go back....

PaulGloor

Know ALL the variables, know the outcome. The only problem is to know all the variables and calculate in real time.

N B

@Norm – Not at all. Feedback control systems already exists in nature, which proves that they are applicable. For that matter, life couldn’t exist without them. The vast number of regulatory systems in the human body are each examples of feedback control, and the entire body with all of its various control systems is a perfect example of the sort of complex system referred to in the documentary (actually, biology is more properly categorized as complex adaptive systems). And we already employ some some rather crude man-made feedback controls to these types of systems – not very well yet, but we try. Treatment of chronic diseases such as type 1 diabetes is one example. In that particular case, the patient monitors his blood glucose and injects insulin to maintain the proper levels. Like I said, it’s pretty crude, but that’s the basic definition of feedback control. The treatment procedure will undoubtedly improve as we learn more and develop better technologies. I strongly suspect that someday, the man-made control systems designed for the human body will out-perform those that we are born with.

It’s definitely much harder to design control systems for things like biology, sociology, economics and others that fall into the category of “complex adaptive systems” because our current understanding of their dynamics is relatively poor. However, our lack of understanding is not indicative of any impenetrable barrier. To my knowledge (and this is my specialty), there are no fundamental barriers that would prevent us from gaining enough knowledge to control these kinds of systems some day. In fact, I can state with certainty that it’s possible to do so for the simplest of reasons: biological systems already do it.

Winston Smith

kind of disturbing how they conflate physics with human invention (war and economic systems) as if the two are inextricably linked and somehow complex natural phenomena justifies human stupidity and suffering. We may develop similar models to try and explain both types of systems but on one side are economic systems, wars and social disorder; all man made. And on the the other, features inherent in the natural world. What we call 'chaos' are the laws of a universe we do not fully understand. They were equally complex in the time of the dinosaurs and long long before then

John Christopher McDonald

That one guys porn 'stache is ridiculous. Good doc though.

melloyeyo

I didn't watch this doc before because got scared by the title and it's classification as a science doc. It is surprisingly good. I thing it's more a Society or Economic doc, but that's the nice thing about it: when a subject is treated in a correct way, it can be classified as a lot of thing because it embarks them all. That is the philosophical way.
Dividing the visions of society in Newtonian and Chaotic is very clever and made me explain many things. I highly recommend this doc.

Norm

@NB
Thank you. As you probably realized, I know very little about the subject and your reply did open my eyes a bit wider.
Have a good day!

CapnCanard

I agree with the experts with regard to global warming et al. Any complex system always has the potential for chaos and systematic breakdown. It is inevitable. Change is unavoidable. The non believers seem to live in a fantasy world and any bad results are never their fault nor will it effect them. They explain it all away by blaming God. The climate change issue is an unstoppable massive tsunami coming straight toward us and our attempts to avoid it are futile. In the same way the economy will not right itself. There is no magic in the market, continual growth at 3% per year is unsustainable and it quickly becomes an exponential function that is as unstoppable as an massive avalanche, a shit storm of stupidity. If there is any blame to be spread around look to Masturbatory Capitalist Economy and the Captains of Industry. Their money will be useless when the shit hits the fan.

hisxmark

The economists are right, there will always be a new equilibrium point. But of course, that point may be one where the human race cannot exist.

hisxmark

We cannot dispute that systems may find new equilibrium conditions, but we should note, in passing, that those new conditions may be such as to preclude the survival of human society or even the survival of the species.

"The magician's first rule: People are stupid." -- Terry Goodkind

Seth Myers

Not bad overall, but this doc should have moved more quickly to the work of Lorenz regarding weather, or at least handled the preceding sections better. The part prior to this confused the concepts of determinism and unpredictability. The narrator speaks as if they are mutually exclusive terms, which was thought so by some in the past and not enough is done to correct this view for the audience. The work of Lorenz and others showed that simple, deterministic equations can behave chaotically; and this is true even if rounding errors are excluded as a factor. This really is the beginning and most interesting concept, at least to me. Without the connection of chaos and determinism, chaos theory seems as simple as stating that systems that behave somewhat at random can have apparently random outcomes.

Seth Myers

There is the butterfly effect and also the butterfly fallacy. An example of the later:

"A thousand butterflies can beat their wings anyway they would like, but it will still be warmer in Costa Rica come January than it is in Toronto."

In other words, system forcing functions can overcome what is spoken of in the doc.

CapnCanard

there are minor problems with your interpretation: Toronto is northern latitude with less sunlight. Plus Costa Rica has potentially volcanic activity. The butterfly's wings may effect temperate zones more so than tropical. It is my understanding that tropical zones may have minor, if any, change whereas Temperate zones could see relative devastation with only minor temperature fluctuations.

1. it equates the unpredictability stemming from chaos theory with uncertainty stemming from non-determinism. In fact, chaotic systems are fully deterministic - we generally just can't measure all relevant variables accurately and adequately enough to be able to model and thus predict them.

2. it suggest, not to subtly, that somehow mathematical thinking is the main foundation on which our cultural notions rest, leading to the ugly suggestion that Germany, France, Russia and the UK entered the first world war, not because they were tangled up in their own greedy power politics, but because they where using Laplacian mathematics. Say what?

Essentially, this documentary says nothing about mathematics. It's basically Gareth Morgan's 'Imaginisation' let loose on history, but forgetting that 'Imaginisation' was all about the metaphorical use of certain mathematical/scientific paradigms, not about the mathematics or science itself.

Mercenarry ForHire

The Chaos shows us that we cant Predict things long Term.
However there's one thing we can do.. Better our self with Knowledge...
That's why Ancient people Valued Knowledge even if it was Simple things :)

Very true, just as they clearly said.Their point, and a corect one I might add, is that the individual variables do not matter, only that the system is doomed to change beyond our ability to predict. You admit yourself the variables are far too many and subtle for us to keep track of.

"it suggest, not to subtly, that somehow mathematical thinking is the main foundation on which our cultural notions rest, leading to the ugly suggestion that Germany, France, Russia and the UK entered the first world war, not because they were tangled up in their own greedy power politics, but because they where using Laplacian mathematics."

True again, and this I can't really defend other to say he was clearly taking poetic liscense to create a sort of metaphor, not really saying these countries entered the war due to thier mathematical calculations. He was trying to impress on the audience the mind set of both Europe and America at the time of this war, which was the mechanical view of the world he described.
This type of mathematical reasoning does however play a huge role in economic, public, and foriegn policy for all developed nations. This inturn directly effects our lives and well being, you can not deny this causal chain if you study politics. Read how mathematics helped shape the thinking of the Soviet union of the fifties and sixties, study how it shaped foriegn and domestic policies in the U.S. during the cold war, how it played into Hitlers plans and ambitions during WW2, how the mathematically based forcast concerning peak oil is shaping world events right now.

"Essentially, this documentary says nothing about mathematics. It's basically Gareth Morgan's 'Imaginisation' let loose on history, but forgetting that 'Imaginisation' was all about the metaphorical use of certain mathematical/scientific paradigms, not about the mathematics or science itself."

I agree, the title is somewhat misleading. But, it does say something about mathematics, something I have experienced first hand being a physics major, recently changed to chemistry major, and that is the transition from classical Newtonian physics to much less intuitive concepts like relativity and the really wierd, unpredictable, and strange QM. By the time we reach QM we are talking about probabilities, no longer linear, cause and effect determinism.

Now we have found that this non-linear behavior can arise in what seem quite simple systems, mostly due to the above mentioned variables. I never progressed far enough in physics to get into much QM, but I see this concept play out in chemistry, specifically equalibrium reactions, all the time. Especially if they are run for long periods of time, usually in industrial situations.The tiny variables effecting rate and equilibrium add up until the system shifts and they have to kill the reaction and start over. This is a very imporatant difference in current mathematical thinking and the math of WW1. In this time they believed that small changes got lost in big systems, and never effected large events, a totally false assumption.

wald0

Here, here, well said!

Ian Denn

life is so boring that its an insult , one hardly care to ask why and how, clearly there is no answers, and humans are indifferent. "past" did exist , future may exist, so what is real? we are left with a zone inside Planck time, a non existing place that makes room for whatever you want to put into it.

GL.

SonofPlato

You make a good point. Chaotic weather patterns can create a beautiful sunny day. The real danger is our current trend of population growth vs finite resources.

Matt van den Ham

It's sort of obvious when you think about it, mathematics is the opposite of chaos. Math wants to endlessly complete pi and solidify's idea's to an exact degree, however when observing a chaotic environment such as space or life itself you'll start to notice that the universe isn't complying to our laws of mathematics. How can math predict how a specie is going evolve in to, look or act like? Nature or the universe is in constant chaos. It's a fearful ideology to accept, that our environment can not be controlled. Humans can not accept this chaotic and instability, just as the concept of space being infinite--how can it be endless? it must end, math/physics say-so.

The acceptance of chaos might sound a recipe for anxiety, but it actually forces you to accept that life isn't as predictable as your mind or intellectuals/intellectualism will have us thinking/believing. When you open your mind to the ideology of chaos you become more observant of the nature's randomness and unpredictability, it gives life a new angle and a potentially fresh-outlook. Don't be afraid, but remain open to change, I think that is the ideology of chaos at the core of it. It allows the mind to think in fluidity rather than boxing everything in this limited or one dimensional language or ideology of understanding.

Our current marketplace has us driven by mathematics so we deem those who are clever at predictability to be very valuable in most society's. However we may be thinking in the wrong direction, or stressing the wrong aspects of human thinking/potential.

alex behrman

Add the role banks played in repeatedly financing wars (very often the same financiers on both sides) and much of the chaos of wars becomes explicable. And don't think for a second bankers are finished playing their games.

Deborah Macaiodh

Question about 1.) Doesn't that imply that it's not actually chaotic? If that's the case, does true chaos exist?

awful_truth

An excellent documentary that should be a wake up call to all those who believe that science can answer everything. The only flaw I could find with it is the idea that laziness brought on the depression of the 1930's. (only indirectly) On the contrary, it was the greed of a relative few who wished to increase their growing fortunes, (theft) while risking the stability of the vast majority through deception,(everyone can be rich - American dream) and propaganda, that caused the depression. To say that it could not be predicted, is akin to our modern day pyramid scheme equivalent. (short term gain for the few, while discarding long term stability for the vast majority) To not see this coming, one would have to had lived their life in a vacuum, absence the insanity of humanity.

awful_truth

@Deborah Macaoidh: Yes, Deborah, true chaos does exist. Daniel has based his premise upon the idea that science can, and will eventually answer everything. Chaos theory, the uncertainty principle of quantum mechanics, and the infinity of PI (science itself) all expose the imperfection, and unpredicability of the universe. Even the greatest scientist of the 20th century (Albert Einstein) could not accept that chance was itself, an inherent aspect of the universe. (god does not play dice with the unvierse)
Thus, Daniel's response should not be judged harshly, but instead is a prime example of a very common human limitation in refusing to accept the unacceptable. (what we want, compared to what is)
In essence, everything in the universe exists for a reason, or it wouldn't exist at all. To embrace this, is to embrace life itself, a tolerance few of us can ever achieve. The best example of this, is trying to get a religious person to accept that god is not perfect, or trying to convince an athiest that god even exists at all. Since both positions are extreme, (polarized) neither accepts the validity of the idea, regarding the truth of everything. Live long, and prosper Deborah!

awful_truth

@alex behrman: Good job Alex separating the wheat from the chaff. There was very little about the economic collapse of 1929, (or 2009) that had anything to do with chance, or chaos theory. On the contrary, we had more than enough information to predict their inevitable arrival. (human nature - greed) Live long and prosper Alex!

Patrick Mackie

1.618

AntiTheist666

Very well said...is it that good? I might need another .00003

LoggerheadShrike

True, but they have to spread this myth of "nobody saw it coming" for all sorts of mistakes. I remember people trying to say that the bloodbath in Iraq couldn't have been predicted, the financial crash of '08 wasn't expected by anyone etc. The reason they have to do this is because they were getting shouted down and told not to do whatever it was depending on the case, they went ahead and did it anyway, and they don't want to be held responsible because they plan to do it again. So they say "oops, who could have guessed?" and pretend like nobody had been begging them to stop.

Our society is being managed by cretins. The vast majority are there because their parents were, and as is typical with that sort of thing, it means they are essentially just a random bunch of people with no particular talent or intelligence. To top it off, they're clueless and live in an insulated world separate from the rest of humanity.

We'd actually be better off if we just stopped the first few hundred people to come along on some random street corner, and let them run the governments and corporations. They'd be roughly the same in terms of competence and intellect, but they'd have more life experience and a better sense of how the world actually operates on the ground.

The human species, has shown such an amazing adaptability by exercising the powers of the cerebral cortex. We survey the world, learn from experience, and use learned probability to predict the future. Sadly, it seems we're like a Saturn 5 rocket, massively powerful, ready to launch into a dynamic promising future, while at the same time chaining ourselves securely to the launch pad, to be incinerated, and blown to bits when the booster is torn apart. This an uncomplimentary situation indeed. Call it passive aggressive, call it the fear of success. It's like a bicycle chain that skips a gear, while peddling at a critical moment, sending us careening into the ditch.

I'll never forget the day Marvin Greenspan, the former chairman of the Federal Reserve, sat in front of our illustrious congress, and testified in front of millions of people that "he had found a flaw in the way, (our model / meaning the conservative/ neoconservative, fascist model ) of the world works". That was the flaw that sent the worlds economy into the ditch, and cost American investors alone, heaven only knows how many trillions of dollars. In the three card monte scramble of deferral, and denial that followed the crash of 2008, the laws of chaos certainly took hold, perhaps if they had considered the math of chaos before hand the catastrophe may have been forestalled, even prevented. Simple answers for simple minds I guess?

awful_truth

This is an absolutely excellent documentary that not only explains the mathematics of chaos, but shows its real world implications regarding the economy, and global warming. This is a 'must see' for everyone who think that the so called 'experts' know what they are talking about.

awful_truth

I am guessing you mean 'Alan Greenspan'? (your point is well made though noboundryman)

noboundryman

Your absolutely right. I did mean Alan Greenspan. I do that with him all the time, and I've been listening to his bull crap for 30 years. Old age sucks. As they say I've forgotten more than some will ever know. Thanks for straightening me out on my rant.

awful_truth

Your welcome. By the way, don't sweat it, that age thing is catching up with me as well. I am in complete agreement with your conclusions about Greenspan. In my opinion, the man was bought off to deregulate for short term greed. When all hell broke loose, his only defense was that his thinking was 'flawed'. In other words, robbery complete! Take care, and best wishes noboundryman.

noboundryman

You my friend are exhibiting all the signs of a
(Defeatist attitude), like the batter who misses every pitch he chooses not to swing at, for fear of striking out.. Thank heaven the forefathers didn't have that attitude, or you would be bowing to the queen today. Thank heaven Nasa, John Kennedy, and the first astronauts didn't say it's inevitable, to hard to think about, to hard to do, when they planned to "send a man to the moon before the decade was through, and return him safely to the earth". Thank heavens the people landing on Normandy, or Iwo Jima beach didn't think it was to hard, or we'd be speaking German, or Japanese, and goose stepping to the forced labor camps, every day : (

It is not inevitable, and the human race has all the capacity to make a huge difference, possibly even reverse the trends of destruction. It requires a different mind set, a different paradigm. Not only can we do it, "we must, do it". The problem is that people are looking at it all the wrong way. The new technologies, new industries, and opportunities, that can and will emerge from the effort will be unbelievable. The space program, and the Apollo program, for instance was anything but certain. It was extremely high risk, extremely expensive, and difficult, but it was done. The after affects of that monumental effort, that most human beings still do not comprehend, is the existence of many of the things we take for granted today: modern plastics, the computer your typing on, new aircraft designs, new medicines, new incites into the world from satellites, the entire international communications industry, and the internet would not be possible except for the courage forward thinking, and determination to embark on an adventure of this magnitude. The technologies that resulted from the (change in paradigm) brought untold riches,and progress. It is most literally a different world today because of it. It is absolutely doable. We have the power, the tools, the physics, the opportunity, and the responsibility to our grandchildren to get it done, "PERIOD"! As my Father use to say, Don't make me come down there"!

bluetortilla

What a fantastic documentary. i cannot imagine at all why its ratings are so low. Without antimatter there would be no universe as we know it, without strife there would be no evolution and without chaos there would be no processes at all.